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 A088931 G.f.: Sum_{n >= 1} ( x^(2^n)/ ((1+x^(2^(n-1)))*Product_{j=0..n-1} (1-x^(2^j)) ) ). 2
 0, 0, 1, 0, 2, 1, 2, 1, 4, 3, 5, 4, 7, 6, 8, 7, 12, 11, 15, 14, 20, 19, 24, 23, 31, 30, 37, 36, 45, 44, 52, 51, 64, 63, 75, 74, 90, 89, 104, 103, 124, 123, 143, 142, 167, 166, 190, 189, 221, 220, 251, 250, 288, 287, 324, 323, 369, 368, 413, 412, 465, 464, 516, 515, 580 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS This is the g.f. for the number of non-squashing partitions with a repeated part, that is, A000123(n) - A088567(n). LINKS Table of n, a(n) for n=0..64. N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, Discrete Math., 294 (2005), 259-274. EXAMPLE x^2/((1 + x)*(1 - x)) + x^4/((1 + x^2)*(1 - x)*(1 - x^2)) + x^8/((1 + x^4)*(1 - x)*(1 - x^2)*(1 - x^4)) + ... MATHEMATICA max = 65; Sum[x^(2^n)/((1+x^(2^(n-1))) Product[1-x^(2^j), {j, 0, n-1}]), {n, 1, Log[2, max] // Ceiling}] + O[x]^(max) // CoefficientList[#, x]& (* _Jean-François Alcover_, Oct 05 2018 *) CROSSREFS Apart from initial terms, same as A088980. Sequence in context: A344255 A344256 A344257 * A088980 A254436 A208548 Adjacent sequences: A088928 A088929 A088930 * A088932 A088933 A088934 KEYWORD nonn AUTHOR _N. J. A. Sloane_, Dec 02 2003 STATUS approved

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Last modified February 29 20:48 EST 2024. Contains 370428 sequences. (Running on oeis4.)